A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F13%3A00065976" target="_blank" >RIV/00216224:14310/13:00065976 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/120873029" target="_blank" >http://dx.doi.org/10.1137/120873029</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/120873029" target="_blank" >10.1137/120873029</a>
Alternative languages
Result language
angličtina
Original language name
A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory
Original language description
An index theorem is a tool for computing the change of the index (i.e., the number of negative eigenvalues) of a symmetric monotone matrix-valued function when its variable passes through a singularity. In 1995, the first author proved an index theorem in which a certain critical matrix coefficient is constant. In this paper, we generalize the above index theorem to the case when this critical matrix may be varying, but its rank, as well as the rank of some additional matrix, are constant. This includesas a special case the situation when this matrix has a constant image. We also show that the index theorem does not hold when the main assumption on constant ranks is violated. Our investigation is motivated by the oscillation theory of discrete symplectic systems with nonlinear dependence on the spectral parameter, which was recently developed by the second author and for which we obtain new oscillation theorems.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP201%2F10%2F1032" target="_blank" >GAP201/10/1032: Difference equations and dynamic equations on time scales III</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Matrix Analysis and Applications
ISSN
0895-4798
e-ISSN
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Volume of the periodical
34
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
228-243
UT code for WoS article
000316855600011
EID of the result in the Scopus database
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